5(x-13)(x+2)=0

Solution for 5(x-13)(x+2)=0 equation:

5(x-13)(x+2)=0

We multiply parentheses ..

5(+x^2+2x-13x-26)=0

We multiply parentheses

5x^2+10x-65x-130=0

We add all the numbers together, and all the variables

5x^2-55x-130=0

a = 5; b = -55; c = -130;
Δ = b2-4ac
Δ = -552-4·5·(-130)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-75}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+75}{2*5}=\frac{130}{10}
=13
$